## 2011.18: The Expected Lifetime of an Extraction Project

2011.18:
G. W. Evatt, P. V. Johnson, P. W. Duck, S. D. Howell and J. Moriarty
(2011)
*The Expected Lifetime of an Extraction
Project.*
Proceedings of the Royal Society A, 467 (2125).
pp. 244-263.
ISSN 1471-2946

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DOI: 10.1098

## Abstract

When a mining company begins extraction from a finite resource, it does so in the presence of numerous uncertainties. One key uncertainty is the future price of the commodity being extracted, since a large enough drop in price can make a resource no longer cost-effective to extract, resulting in the mine being closed down. By specifying a stochastic price process, and implementing a financial-type model which leads to the use of partial differential equations, this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period, and derives the associated expected lifetime of extraction. An approximation to the abandonment price is described, which enables a closed-form solution to be derived for the probability of operational success and expected lifetime. This approximation compares well with the full solution obtained using a semi-Lagrangian numerical technique.

Item Type: | Article |
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Uncontrolled Keywords: | Partial Differential Equations, Finite Resource Valuations, Feynman-Kac, Real Options. |

Subjects: | MSC 2000 > 35 Partial differential equations |

MIMS number: | 2011.18 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 18 February 2011 |

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